Time Complexity Analysis of Binary Search Trees Operations

Unit 1: Growth of Functions, Recurrence Relations

• Functions Used in Analysis
• Asymptotic Notations
• Asymptotic Analysis
• Solving Recurrences Using Recursion Trees
• Master Theorem

Unit 2: Arrays, Linked Lists, Stacks, Queues, Deques

• Introduction to Array Data Structure
• Array Operations
• Applications of Array Data Structures
• Introduction to Sorting in Array
• Two-dimensional Arrays
• Dynamic Allocation of Arrays
• Singly-linked Lists
• Doubly Linked Lists
• Circularly Linked Lists
• Stacks: Stack as an ADT
• Implementing Stacks Using Arrays
• Implementing Stacks Using Linked Lists
• Applications of Stacks
• Queues: Queue as an ADT
• Implementing Queues Using Arrays
• Implementing Queues Using Linked Lists
• Double-ended Queue as an ADT
• Implementing Double-ended Queues Using Linked Lists
• Time Complexity Analysis of Arrays, Linked Lists, Stacks and Queues

Unit 3: Recursion

• Recursive Functions
• Linear Recursion
• Binary Recursion

Unit 4: Trees, Binary Trees

• Trees: Definition and Properties
• Tree Traversal Algorithms and Their Time Complexity Analysis
• Binary Trees: Definition and Properties
• Traversal of Binary Trees and Their Time Complexity Analysis

Unit 5: Binary Search Trees, Balanced Search Trees

• Insertion of Binary Search Trees
• Deletion of Binary Search Trees
• Search Operations of Binary Search Trees
• Time Complexity Analysis of Binary Search Trees Operations
• Insertion of Balanced Search Trees
• Search Operations of Balanced Search Trees
• Time Complexity Analysis of Balanced Search Trees Operations

Unit 6: Binary Heap, Priority Queue

• Introduction to Binary Heaps
• Heap Operations
• Implementing Heaps
• Priority Queue as an ADT
• Time Complexity Analysis of Priority Queues

Unit 7: Graph Representations and Traversal Algorithms

• Graph as an ADT
• Data Structures for Graphs
• Traversal of Graphs
• Directed Graphs
• Time Complexity Analysis of Graphs